Leakage Flow Research Articles

Thermo-fluid dynamic numerical analysis of vestibule functions in a solar updraft tower

Solar updraft towers (SUTs) represent a promising avenue for renewable energy generation, leveraging solar energy to drive their operation. Although the collector of SUTs is generally vacant, ongoing research have focused on auxiliary structures inside the collector aimed at enhancing the overall efficiency. This study delved into the computational fluid dynamics (CFD) analysis of a SUT model featuring a 5 m radius collector and a 12 m height chimney. Specifically, we investigated the vestibule functions which created by implementing baffle inside the SUT collector with various radial locations. Through rigorous examination, the thermo-fluid dynamic effects of both roof-mounted and bottom-mounted baffles on SUT performance were explored, aiming to ascertain the optimal vestibule parameters. The vestibule was found to mitigate the backward flow leakage, isolate the inner room from the outside air, and enhance the heat exchange efficiency of the main flow. Notably, when the roof-mounted baffle was positioned at a radial location of 4.5 m, a remarkable 11.4 % and 28.1 % increase in the mass flow rate at the chimney outlet and kinetic power were achieved, respectively. These findings highlight the significant performance improvements achievable through the incorporation of a vestibule within SUTs of a given scale.

Numerical investigation of bimodal tip clearance effect on the lift-drag and flow characteristics of a hydrofoil

Tip leakage flow has adverse effect on energy conversion of the hydraulic machinery. The new tip clearance structure based on Bimodal Gaussian function is designed to reduce tip leakage vortex. The effects of bimodal structure with different amplitudes and arrangement positions on lift-drag and flow characteristics are studied. The results show that the maximum rise of the lift-drag ratio reaches 5.88% when the bimodal structure amplitude is equal to the tip clearance size. The bimodal structure reduces the outflow velocity at the peak and forms a smooth streamline, which weakens the entrainment with the mainstream. The location of the bimodal structure far away from leading edge helps to produce smooth streamlines and make the flow field smoother, and reduces the area of high turbulent kinetic energy region near leading edge and in tip clearance outflow region significantly. The arrangement position of bimodal structure close to leading edge can produce a low-speed zone or a recirculation zone in the mainstream, which can block the mainstream flow and reduce the energy characteristics of the hydrofoil.

Synchronous PIV measurements of a self-powered blood turbine and pump couple for right ventricle support

A blood turbine-pump system (iATVA), resembling a turbocharger was proposed as a mechanical right-heart assist device without external drive power. In this study, the iATVA system is investigated with particular emphasis on the blood turbine flow dynamics. A time-resolved 2D particle image velocimetry (PIV) set-up equipped with a beam splitter and two high speed cameras, allowed simultaneous recordings from both the turbine and pump impellers at 7 different phased-locked instances. The iATVA prototype is 3D printed using an optically clear resin following our earlier PIV protocols. Results showed that magnetically coupled impellers operated synchronously. As the turbine flow rate increased from 1.6 to 2.4 LPM, the rotational speed and relative inlet flow angle increase from 630 to 900 rpm, and 38 to 55% respectively. At the trailing edges, backflow region spanned 3/5 of the total passage outlet flow, and an extra leakage flow was observed at the leading edge. For this early turbine design, approximately, 75% of the turbine blade passage was not contributing to the impulse operation mode. The maximum non-wall shear rate was ~ 2288 s−1 near to the inlet exit, which is significantly lower than the commercial blood pumps, encouraging further research and blood experiments of this novel concept. Experimental results will improve the hydrodynamic design of the turbine impeller and volute regions and will be useful in computational fluid dynamics validation studies of similar passive devices.

Stability enhancement using a new combined casing treatment strategy in an ultra-highly loaded transonic compressor rotor

Low-reaction compressors are promising for achieving high loads but face severe flow instability challenges. This study investigates a low-reaction transonic compressor rotor using casing treatment technologies to control unstable flow dynamics precisely. First, a design integrating self-recirculating and circumferential groove casing treatments near the leading edge is implemented. This design enhances flow capacity at the tip passage inlet. However, it causes a “stall transposition” phenomenon. The unstable flow structures shift from shock-tip leakage vortex interactions at the front to corner separation at the rear. Consequently, the stall mechanism transitions from an end-wall stall to a blade stall. To address this issue, a new casing treatment layout is proposed. Grooves are added after the mid-chord of the initial front casing configuration. This adaptation suppresses emerging unstable flow structures and extends the stall margin by approximately 12.07 %. Detailed flow field analysis shows that the rear grooves effectively reduced the trailing edge separation vortex. They also limit downstream corner separation and mitigate disturbances from tip leakage flows in the rear of the passage.

Experimental and numerical investigation on middle passage gap leakage with different mass flow rate and injection angle on turbine endwall

Regarding the actual installation feature of the blades and disk using tenon and mortise, the middle passage gap exists between the adjacent blades and the leakage flows out of the gap, cooling the endwall. To explore the balance between the aerodynamic and cooling performance on blade endwall in turbine cascade, this paper investigated the effect of middle passage gap leakage under various mass flow rate and injection angle configurations. Film cooling effectiveness measurement was performed with pressure-sensitive paint technique in a five-passages linear cascade. The mass flow ratio of middle passage gap leakage ranged from 0.5 % to 1.5 % with the injection angle (αm) ranging from −20° to 20°. A combined approach utilizing numerical simulations to elucidate detailed aerodynamic loss mechanisms and experimental results of middle passage gap leakage was employed. The results show that increasing the mass flow rate of middle passage gap leakage does not suppress mainstream intrusion phenomenon. Cases with injection angle generally show improved cooling performance compared to the non-injection case (αm = 0°). The least improvements are 19 % and 27.9 % for mass flow rates of 0.5 % and 1.0 %, respectively. The case with an injection angle of 20° demonstrates the best comprehensive performance, achieving higher area-averaged cooling effectiveness and lower aerodynamic loss (1.2 % and 18.9 % decrease for mass flow rates of 0.5 % and 1.0 %).

Effects of rim seal exit geometry on the cooling characteristics of turbine endwall and blade suction side

For a turbine blade endwall, the leakage (purge flow) exits through rim seal to prevent hot gas ingress and provide some cooling to the endwall. However, changes in the rim seal geometry will inevitably affect the leakage flow over the endwall. To obtain a clearer and quantitative understanding of the effect of rim seal variation on the cooling performance and flow structure, this paper investigated the effects of width and inclined angle of rim seal exit geometry, as well as the flow structure inside the gap and above the passage. A correlation fitting was constructed using the area-averaged cooling effectiveness to quantify the cooling performance on the suction side. The results indicate that the cooling performance of endwall is not sensitive to changes in width. However, a decrease in the inclined angle benefits the inhibition of the cavity vortex, prevents the gas ingress and improves the cooling performance overthe endwall. The cooling performance of blade suction side is sensitive to the leakage mass flow ratio. As the mass flow rate increases from 0.5 % to 1.0 % and 1.5 %, the area-averaged cooling effectiveness on suction side for original case increases by 44.4 % and 30.7 %. The correlation established for the cooling of suction side shows a good fit, which provide a possible evaluation method for cooling design.

Impact of non-axisymmetric tip clearance on the aerodynamic and aeroelastic stabilities of a transonic compressor

The aerodynamic and flutter effects caused by the circumferential non-uniform tip clearances from the non-axisymmetric casing geometry, which are more representative of real operational conditions, should receive more attention. In this paper, sensitivity analyses on clearance and non-uniformity regarding rotor performance are conducted. The isentropic efficiency, total pressure ratio and stability margin of the rotor are reduced by 1.96%, 1.06% and 6.76% for an increase of tip clearance by 1% tip chord, respectively. The non-axisymmetric configuration reconfigures the interaction between leakage flow and mainstream in each rotor passage and alters the strength and influence range of the low-speed separation region generated by shock wave. The phase lag phenomenon observed in the aerodynamics of the non-axisymmetric layout also manifests in the aeroelastic effects but requires a larger phase shift at the maximum clearance sector, owing to the longer timescales for flow adjustment relative to the local tip gap considering the flow-induced vibration. Clearance sensitivity on flutter stability varies with the direction of the traveling wave: under forward traveling conditions, damping values initially decrease and then increase with increasing rotor tip clearance; while under backward traveling condition, blade damping linearly decreases with increasing rotor tip clearance. Additionally, variations in flow conditions and nodal diameters affect flutter stability by altering the position of shock waves and their work on the suction surface of the rotors. The mechanism responsible for unsteady flows induced by non-axisymmetric clearances from the casing ovalization on flutter stability is discussed for the first time in this paper, which can guide the industry to evaluate its impact.

The Influence of the Fire Point on the Thermal Dynamic Disaster in the Goaf

A thermal dynamic disaster in the goaf is one of the most serious coal mine disasters formed by coal spontaneous combustion and gas interweaving. However, the influence of the high-temperature hidden fire source formed in the goaf on the evolution law of thermal dynamic disasters is not clear, and effective prevention and control measures cannot be taken. Therefore, this paper uses the experimental platform of thermal dynamic disaster in the goaf to study the influence of different fire point positions on the development of thermal dynamic disaster in the goaf through a similar simulation experiment of thermal dynamic disaster evolution in the goaf and analyzes the corresponding relationship between temperature and CO concentration in the upper corner. The results show that under different locations of heat source, the high-temperature heat source of coal spontaneous combustion migrates to the air leakage side with sufficient oxygen supply, and an oxygen-poor circle is formed near the ignition point. Under the action of air leakage flow, CH4 accumulates in the deep part of the goaf on the return air side. Due to the increase in coal, part of CH4 is produced, which leads to the increase in concentration of CH4 at the ignition point. Under the action of different heat sources, the changing trend of concentration of CO and temperature in the return air corner is the same, but the temperature change in the return air corner shows a lag compared with the change in the concentration of CO, so concentration monitoring of CO can reflect the evolution process of the fire field in the goaf more quickly than temperature monitoring.

PIV investigation of stalled flow field near the blade rim region of mixed-flow pump under different tip clearances

In order to further explore the physical mechanism of rotating stall induced by different rim leakage flow intensification, the velocity distribution of the stall flow field of the mixed flow pump under different rim clearance scales was obtained by Particle Image Velocimetry technology. By comparing the flow structure under different shooting sections, different phases and different working conditions, the influence of rim clearance scale on the flow field near the wall of the mixed flow pump was revealed. The results show that under the design flow conditions, there is an obvious reflux phenomenon near the hub of the guide vane inlet of the mixed flow pump under the four kinds of rim clearance, but the intensity is weak, and it does not affect the main flow field in the impeller channel. With the increase of rim clearance scale, the leakage flow intensity also increases, and the main flow area affected by the TLV structure also increases. In the deep stall condition, the reflux vortex at the inlet of the guide vane of the mixed flow pump still exists at each clearance, but the unsteady flow structure begins to appear inside, especially the large secondary vortex structure formed at the guide vane inlet, which seriously blocks the main flow. With the increase of the rim clearance, the flow field at the inlet of the guide vane is also obviously affected, and the secondary vortex core gradually moves towards the end wall area, resulting in an increase in the blocked area in the flow field. At the same time, the unsteady flow intensity of the flow field shows a nonlinear increasing trend. The unsteady strength of flow field increases rapidly with small gap impellers, while the unsteady strength changes slowly with large gap impellers. This study provides a reference for optimizing the rim clearance of mixed-flow pump and improving the efficiency of mixed-flow pump.

Innovative foresight for water utilities asset management using PRISM software

Our analysis aims to better understand water losses by developing a specific methodology for estimating water leak flow rates and durations. Additionally, it aims to improve asset management practices for drinking water utilities by forecasting the costs and benefits of investment and operational decisions on the network. Current utility practices are compared to a "do nothing" policy and to the potential effective asset management policies proposed by an artificial neural network (ANN) based software, PRISM. Applied to four utilities in France, our methodology provides valuable insights for enhancing water loss estimates and finding trade-off asset management policies.

Numerical Investigation of Sediment Erosion in Guide Vanes of Francis Turbine with Experimental Validations

Abstract Serving as crucial elements within the distributor of Francis turbines, guide vanes aid in converting pressure energy into velocity energy. Additionally, they are responsible for directing water into the runner at the appropriate angle and quantity. The existence of a clearance gap in the guide vanes leads to the development of a leakage flow due to the pressure variation between the two sides. This leakage flow develops into a vortex, which interacts with sediment-laden flow and causes erosion of the guide vane as well as the runner. This study conducts a comprehensive analysis of erosion patterns in the guide vanes of a 2-kW model Francis turbine. Employing a dual approach that combines both experimental and computational methods, the investigation focuses on the impact of clearance gaps on erosion. The numerical study focuses on two cases, one incorporating a 2 mm clearance gap on the hub side of the guide vane and the other without the clearance gap. Both studies report erosion initiating from the mid-section and extending to the trailing edge at the suction side of the guide vane. Noteworthy is the leakage flow from the pressure side to the suction side of the blade, which, when converging with the main flow, disturbs the primary flow pattern and forms vortices, leading to erosion. This research also shows that the results from both the experimental and numerical analyses are in agreement.

Effect of the leakage flow through guide vanes on the erosion pattern and performance of Francis runner

Abstract The role of hydropower as a renewable energy source is well understood. However, due to the geological characteristics of certain regions, hydropower systems there are facing a unique challenge of excessive sedimentation in rivers. A significant number of research works were performed in the past, which focused on the effects of sediments on the turbine components, that includes reduction in efficiency of the turbine and increase in the erosion wear. Experimental studies of erosion in laboratory conditions are usually limited by several characteristics that affect erosion and complications of handling sediments. As a result, these investigations are normally carried out in a simplified apparatus. This study focuses on using a non-recirculating type of sediment erosion test rig, where a model of Francis turbine is used for experimental investigations. Previous studies have shown that in the case of Francis turbines, erosion occurs in the clearance gap of guide vanes, which increases the size of the gap. The flow from the pressure side of the guide vane is driven into the suction side due to the pressure difference between the two sides. This leakage flow ultimately develops into a vortex filament and hits the runner blades towards the hub and shroud. In this study, the erosion pattern of the runner blades towards these locations are studied by using color coatings. A clearance gap of 4 mm has been created in the guide vane and the consequent impact on the erosion and efficiency of the turbine are studied. The objective is to isolate the effects of leakage flow on erosion in the runner inlet, as well as the overall performance of the Francis turbine. The effect has been observed in terms of increased flow rate, decreased efficiency and erosion in the leading edge of the runner.

Fast flow field prediction of pollutant leakage diffusion based on deep learning.

Predicting pollutant leakage and diffusion processes is crucial for ensuring people's safety. While the deep learning method offers high simulation efficiency and superior generalization, there is currently a lack of research on predicting pollutant leakage and diffusion flow field using deep learning. Therefore, it is necessary to conduct further studies in this area. This paper introduces a two-level network method to model the flow characteristics of pollutant diffusion. The proposed method in this study demonstrates a significant enhancement in flow field prediction accuracy compared to traditional deep learning methods. Moreover, it improves computational efficiency by over 800 times compared to traditional computational fluid dynamics (CFD) methods. Unlike conventional CFD methods that require grid expansion to calculate all operation conditions, the deep learning method is not confined by grid limitations. While deep learning methods may not entirely replace CFD methods, they can serve as a valuable supplementary tool, expanding the versatility of CFD methods. The findings of this research establish a robust foundation for incorporating deep learning methods in addressing pollutant leakage and diffusion challenges.

Unsteady measurement in a transonic axial compressor with optimized axial slot casing treatment

Casing treatment has been widely adopted to enhance the operating range of compressors by extending the stall margin. In this article, a high-precision experimental investigation was conducted in a transonic compressor. Unsteady pressure is measured in the casing wall using a cluster of time-resolved transducers with axial and circumferential spatial resolution. The experimental data show that the optimized axial slot casing treatment improves the stall margin without peak efficiency penalty for all measured speedlines. A comprehensive flow field analysis indicates that the surge boundary of transonic compressor is sensitive to the position of shock wave and tip leakage flow. After the application of optimized axial slot casing treatment, the flow structure can be significantly modified, which specifically manifests as both the mitigation in shock wave detachment and redistribution of tip leakage flow trajectory toward the trailing edge of the blade. Furthermore, power spectral density analysis is conducted to examine the unsteady effect. The amplitude of characteristic frequency band induced by the unsteady fluctuation of tip leakage flow and shock wave is considerably suppressed, which can also be regard as the stability enhancement mechanism of casing treatment.

Experimental study of sediment erosion in Francis runner using a non-recirculating test rig

Abstract The problem of sediment erosion in hydraulic turbines has posed challenges in design, operation and maintenance of hydraulic machinery. A study was conducted with a 2 kW model Francis runner for investigating the erosion prone locations. The runner and guide vanes were coated with four different coats of colour (red, yellow, green, and blue). The system was then operated in sediment-laden condition with an average concentration of sediment particles of about 24000 ppm. The runner was operated in sediment-laden conditions for 36 hours and the observations were made after each 4 hours of operation. With increasing hours of operation, the colour coating of the runner was eroded at specific locations and a pattern was revealed showing the areas affected by erosion. The erosion was mostly observed at the trailing edge of the pressure side and the junction of the suction side of the blade and hub. Erosion on the hub was observed towards the leading edge of the runner in the area close to the suction side and the region near the trailing edge of blade. Similarly, the guide vanes were eroded at the pressure side of the leading edge and the trailing edge of the suction side. The causes of erosion were identified as high velocity and acceleration of sediment particles, inter-blade vortex, and vortex due to leakage flow.

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

This study explores the implementation of physics-informed neural networks (PINNs) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The segregated PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e. porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features, including flow leakage, channeling effect and wake recirculation was investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data was considered in this study. Results showed that the PINN model predictions with second-order internal training data achieved high accuracy for the prominent flow features compared to the RANS data, within a 20% L2 norm error of second-order statistics in the solid block case. In addition, for the porous block case, providing training data at the porous-fluid interface showed errors of 18.04% and 19.94% for second-order statistics, representing an increase in prediction accuracy by 7% compared to without interface training data. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.

Prediction of icicles on lining surface in high-speed railway tunnel in severe cold region based on the characteristics of daily temperature fluctuation

：Icicles in high-speed railway tunnels in cold regions pose a serious threat to operational safety. Tunnels with long lengths and large sizes require manual inspection, generating considerable work and expense for operation management. To reduce the workload of icicle inspection and guide manual deicing, a growth and development model of tunnel icicles was developed based on a tunnel icicle simulation system, and a tunnel lining icicle prediction and warning system was established, that provides guidance for deicing by predicting the range and development degree of tunnel icicles. The icicle simulation test shows that there is an obvious division of icing and non-icing area in the tunnel, and the boundary of the division is −5 °C. There is an optimum temperature range for the growth and development of icicle in tunnels. Under daily temperature fluctuations, the icicles grow back after being removed. A model for degree of icicle development was established. The degree of icicle development is affected by leakage flow, daily fluctuation amplitude of temperature, and daily average temperature. The smaller the daily temperature fluctuation and the closer the daily average temperature to the optimum temperature for icicle growth, the better the development of icicle. Based on the icicle development model, a prediction and warning method for icicles in tunnel was developed. Based on the network of instruments measuring and reporting temperature, the real-time temperature distribution of the tunnel was obtained, combined with the leakage distribution and volume in the tunnel, the icicles section and the icicles severity of the tunnel were obtained by analyzing the icicle growth model embedded in the system, providing guidance for the inspection of icicles in the tunnel. A comparison shows that the icicle prediction and warning system can reduce the walking inspection workloads by half.

Investigation of Reynolds number effects on flow stability of a transonic compressor using a dynamic mode decomposition method

With the continuous increase in aircraft flight altitude, low Reynolds number effects in high-altitude environments significantly impact the stability of compressor operation. In this study, dynamic mode decomposition (DMD) of the flow field at various time instances near stall conditions in a transonic compressor was performed to investigate the influence of Reynolds number (Re) effects on critical flow characteristics and instability mechanisms. The results indicate that under different Reynolds number index (RNI) conditions near stall conditions, the frequency of tip leakage flow varies. Under high RNI condition, the influence of tip leakage flow is concentrated mainly from the leading edge to the mid-chord. The stall mode is primarily caused by the interaction of shock with the Tip Leakage Vortex, resulting in the breakdown of the vortex. The development of vortex structures inside the passage leads to a delay in the flow field response to blade passing. Under low RNI condition, the tip clearance leakage flow is stronger, with a relatively reduced influence from the leading edge to the mid-chord and an increased impact from the mid-chord to the trailing edge. The main cause of the stall mode is the circumferential movement of vortex structures, causing secondary leakage over adjacent blade tip clearances. The blockage formed by vortex structures within the passage is weaker, and the flow field response to blade passing remains consistent with the blade passing frequency. However, as stall develops further, the flow field response significantly decreases.

Visualization and Quantification of Facemask Leakage Flows and Interpersonal Transmission with Varying Face Coverings

Although mask-wearing is now widespread, the knowledge of how to quantify or improve their performance remains surprisingly limited and is largely based on empirical evidence. The objective of this study was to visualize the expiratory airflows from facemasks and evaluate aerosol transmission between two persons. Different visualization methods were explored, including the Schlieren optical system, laser/LED-particle imaging system, thermal camera, and vapor–SarGel system. The leakage flows and escaped aerosols were quantified using a hotwire anemometer and a particle counter, respectively. The results show that mask-wearing reduces the exhaled flow velocity from 2~4 m/s (with no facemask) to around 0.1 m/s, thus decreasing droplet transmission speeds. Cloth, surgical, and KN95 masks showed varying leakage flows at the nose top, sides, and chin. The leakage rate also differed between inhalation and exhalation. The neck gaiter has low filtration efficiency and high leakage fractions, providing low protection efficiency. There was considerable deposition in the mouth–nose area, as well as the neck, chin, and jaw, which heightened the risk of self-inoculation through spontaneous face-touching. A face shield plus surgical mask greatly reduced droplets on the head, neck, and face, indicating that double face coverings can be highly effective when a single mask is insufficient. The vapor–SarGel system provided a practical approach to study interpersonal transmission under varying close contact scenarios or with different face coverings.

A Computational Analysis of Turbocharger Compressor Flow Field with a Focus on Impeller Stall

Understanding the flow instabilities encountered by the turbocharger compressor is an important step toward improving its overall design for performance and efficiency. While an experimental study using Particle Image Velocimetry was previously conducted to examine the flow field at the inlet of the turbocharger compressor, the present work complements that effort by analyzing the flow structures leading to stall instability within the same impeller. Experimentally validated three-dimensional computational fluid dynamics predictions are carried out at three discrete mass flow rates, including 77 g/s (stable, maximum flow condition), 57 g/s (near peak efficiency), and 30 g/s (with strong reverse flow from the impeller) at a fixed rotational speed of 80,000 rpm. Large stationary stall cells were observed deep within the impeller at 30 g/s, occupying a significant portion of the blade passage near the shroud between the suction surface of the main blades and the pressure surface of the splitter blades. These stall cells are mainly created when a substantial portion of the inlet core flow is unable to follow the impeller’s axial to radial bend against the adverse pressure gradient and becomes entrained by the reverse flow and the tip leakage flow, giving rise to a region of low-momentum fluid in its wake. This phenomenon was observed to a lesser extent at 57 g/s and was completely absent at 77 g/s. On the other hand, the inducer rotating stall was found to be most dominant at 57 g/s. The entrainment of the tip leakage flow by the core flow moving into the impeller, leading to the generation of an unstable, wavy shear layer at the inducer plane, was instrumental in the generation of rotating stall. The present analyses provide a detailed characterization of both stationary and rotating stall cells and demonstrate the physics behind their formation, as well as their effect on compressor efficiency. The study also characterizes the entropy generation within the impeller under different operating conditions. While at 77 g/s, the entropy generation is mostly concentrated near the shroud of the impeller with the core flow being almost isentropic, at 30 g/s, there is a significant increase in the area within the blade passage that shows elevated entropy production. The tip leakage flow, its interaction with the blades and the core forward flow, and the reverse flow within the impeller are found to be the major sources of irreversibilities.